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Simplifying -16x2 + 60x = -255 Reorder the terms: 60x + -16x2 = -255 Solving 60x + -16x2 = -255 Solving for variable 'x'. Reorder the terms: 255 + 60x + -16x2 = -255 + 255 Combine like terms: -255 + 255 = 0 255 + 60x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -15.9375 + -3.75x + x2 = 0 Move the constant term to the right: Add '15.9375' to each side of the equation. -15.9375 + -3.75x + 15.9375 + x2 = 0 + 15.9375 Reorder the terms: -15.9375 + 15.9375 + -3.75x + x2 = 0 + 15.9375 Combine like terms: -15.9375 + 15.9375 = 0.0000 0.0000 + -3.75x + x2 = 0 + 15.9375 -3.75x + x2 = 0 + 15.9375 Combine like terms: 0 + 15.9375 = 15.9375 -3.75x + x2 = 15.9375 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 15.9375 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 15.9375 + 3.515625 Combine like terms: 15.9375 + 3.515625 = 19.453125 3.515625 + -3.75x + x2 = 19.453125 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 19.453125 Calculate the square root of the right side: 4.410569691 Break this problem into two subproblems by setting (x + -1.875) equal to 4.410569691 and -4.410569691.Subproblem 1
x + -1.875 = 4.410569691 Simplifying x + -1.875 = 4.410569691 Reorder the terms: -1.875 + x = 4.410569691 Solving -1.875 + x = 4.410569691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 4.410569691 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 4.410569691 + 1.875 x = 4.410569691 + 1.875 Combine like terms: 4.410569691 + 1.875 = 6.285569691 x = 6.285569691 Simplifying x = 6.285569691Subproblem 2
x + -1.875 = -4.410569691 Simplifying x + -1.875 = -4.410569691 Reorder the terms: -1.875 + x = -4.410569691 Solving -1.875 + x = -4.410569691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -4.410569691 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -4.410569691 + 1.875 x = -4.410569691 + 1.875 Combine like terms: -4.410569691 + 1.875 = -2.535569691 x = -2.535569691 Simplifying x = -2.535569691Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.285569691, -2.535569691}
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